Merely Possible Possible Worlds

Mere Possibilities ◽

10.23943/princeton/9780691147123.003.0002 ◽

2012 ◽

Author(s):

Robert Stalnaker

Keyword(s):

General Model ◽

Possible Worlds ◽

Logical Space ◽

Modal Properties ◽

Minimal Theory

This chapter first sketches a minimal theory of propositions—one that ascribes to propositions just the structure that anyone who is willing to talk of propositions at all must ascribe to them. It extends the minimal theory by adding some assumptions about the modal properties of propositions and possibilities, and then sketches a general model of logical space that makes room for merely possible possibilities. Next, it considers the relation between models and the reality that they purport to model and the extent to which our theory of propositions and possibilities provides a realistic semantics. Finally, it responds to some arguments against the thesis that propositions may exist contingently.

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The Metaphysics of Propositions

10.1093/oxfordhb/9780199935314.013.26 ◽

2017 ◽

Author(s):

Jeffrey C. King

Keyword(s):

Possible Worlds ◽

Direct Reference ◽

Bertrand Russell ◽

Gottlob Frege ◽

Modal Properties

Propositions have been long thought by many philosophers to play a number of important roles. These include being the information conveyed by an utterance of a sentence, being the primary bearers of truth and falsity, being the possessors of modal properties like being possible and necessary, and being the things we assume, believe, and doubt. This article canvases significant attempts by philosophers to say what sorts of things propositions are. First, the classical views of propositions advanced by Gottlob Frege and Bertrand Russell are considered. Second, the view of propositions as sets of possible worlds is discussed. Next, views of propositions arising out of work on direct reference are discussed. The article closes with a discussion of more recent views of propositions.

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On the Humphrey Objection to Modal Realism

Grazer Philosophische Studien ◽

10.1163/18756735-000032 ◽

2018 ◽

Vol 95 (2) ◽

pp. 159-179 ◽

Cited By ~ 1

Author(s):

Michael De

Keyword(s):

Possible Worlds ◽

Modal Realism ◽

Modal Properties

An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two potential answers to the objection so understood and concludes that only one of them has a chance of succeeding.

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Incarnation, Divine Timelessness, and Modality

TheoLogica An International Journal for Philosophy of Religion and Philosophical Theology ◽

10.14428/thl.v2i3.2283 ◽

2019 ◽

Vol 3 (1) ◽

pp. 88-112

Author(s):

Emily Paul

Keyword(s):

Possible Worlds ◽

Modal Realism ◽

Logical Space ◽

Christian Doctrine ◽

Son Of God ◽

Classical Theism ◽

Modal Claim ◽

Modal Variation ◽

Genuine Modal Realism

A central part of the Christian doctrine of the incarnation is that the Son of God ‘becomes’ incarnate. Furthermore, according to classical theism, God is timeless: He exists ‘outside’ of time, and His life has no temporal stages. A consequence of this ‘atemporalist’ view is that a timeless being cannot undergo intrinsic change—for this requires the being to be one way at one time, and a different way at a later time. How, then, can we understand the central Christian claim that the Son of God ‘becomes’ human? This paper examines one such explanation, drawn from a brief remark by Brian Leftow: the Word takes on flesh by exhibiting modal variation with regards to the incarnation. On this account, a timeless God ‘becomes’ incarnate simply due to variation across logical space: at some possible worlds He is incarnate and at others He is not. Modal variation need not, therefore, require temporality: it only requires variation across (static) possible worlds. I draw out the problems with Leftow’s modal claim under the heads of Ersatzism and Genuine Modal Realism about possible worlds, respectively. I argue that in both instances, Leftow’s desired cross–worldly variation of the Son’s incarnation cannot be achieved.

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THE BOREL COMPLEXITY OF ISOMORPHISM FOR O-MINIMAL THEORIES

Journal of Symbolic Logic ◽

10.1017/jsl.2017.17 ◽

2017 ◽

Vol 82 (2) ◽

pp. 453-473 ◽

Cited By ~ 1

Author(s):

RICHARD RAST ◽

DAVENDER SINGH SAHOTA

Keyword(s):

Lower Bounds ◽

General Model ◽

Isomorphism Problem ◽

Linear Orders ◽

Minimal Theory ◽

Borel Complexity ◽

Image Position ◽

Countable Models

AbstractGiven a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the isomorphism problem for linear orders into the isomorphism problem for models of T. This is done by constructing models with specific linear orders in the tail of the Archimedean ladder of a suitable nonsimple type.If the theory admits no nonsimple types, then we use Mayer’s characterization of isomorphism for such theories to compute invariants for countable models. If the theory is small, then the invariant is real-valued, and therefore its isomorphism relation is smooth. If not, the invariant corresponds to a countable set of reals, and therefore the isomorphism relation is Borel equivalent to F2.Combining these two results, we conclude that $\left( {{\rm{Mod}}\left( T \right), \cong } \right)$ is either maximally complicated or maximally uncomplicated (subject to completely general model-theoretic lower bounds based on the number of types and the number of countable models).

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On Emily Paul on Brian Leftow

TheoLogica An International Journal for Philosophy of Religion and Philosophical Theology ◽

10.14428/thl.v3i2.20543 ◽

2019 ◽

Vol 3 (2) ◽

pp. 140-151

Author(s):

Matthew James Collier

Keyword(s):

Possible Worlds ◽

Logical Space ◽

Compelling Argument ◽

Modal Variation

Emily Paul has recently argued that Brian Leftow’s account of why the import of God’s becoming Incarnate is not temporal but modal fails. She argues that Leftow’s required modal variation is not satisfied. That is, we do not have the required variation across logical space concerning the Incarnation. Paul examines her argument on two possible worlds theories: theistic ersatzism and (what I call) Lewisian theism. She thinks that both possible worlds theories face difficulties. I argue that Paul fails to provide a compelling argument against Leftow because, firstly, her defence of one her premises fails, and, secondly, she misjudges what is required for some of Leftow’s claims to be true. I also argue that some of the problematic consequences that Paul raises for theistic ersatzism and Lewisian theism either are not problematic or can be avoided.

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